We study identifying assumptions in the random utility model, the standard empirical paradigm in modern economics. Our main result characterizes those ex-ante restrictions which lead to identification. Our characterization utilizes a simple class of mass preserving swaps. These swaps take in two preferences which share a common upper and lower contour set but disagree on their ordering within these two sets. The output of this procedure is two preferences which are created by swapping the matching between the ordering of the upper and lower contour sets of the two input preferences. Any two distributions over preferences are observationally equivalent if and only if one can be recovered from the other by a finite sequences of such swaps. It follows that a random utility model is identified if it does not contain any two such distributions over preferences.

Dating back to at least [Samuelson, 1938], the study of the testable implications of models of individual preference and decision making has occupied a central position within both empirical and theoretical economics. In behavioral and decision theory, experimental falsification, or the discovery of 'paradoxes' documenting widespread empirical inconsistency with respect to various axioms, has been a long-standing driver of progress.1 Related puzzles in macroeconomics and finance (e.g. the equity premium puzzle, see Mehra and Prescott 1985) have similarly led to the creation of new theories of individual behavior (Constantinides 1990, Epstein and Zin 1989).